Does the generalized second law hold in the form of time derivative expression?

TL;DR

This paper examines the validity of the generalized second law in two-dimensional black hole spacetime, revealing potential violations of its time derivative form and proposing possible resolutions.

Contribution

It formulates a time derivative version of the generalized second law and discusses conditions under which it may fail, offering insights into its validity in black hole physics.

Findings

The law might become invalid in certain conditions.

A method to resolve the potential violation is proposed.

The study is model-independent, focusing on 2D black hole spacetime.

Abstract

We investigate whether the generalized second law is valid, using two dimensional black hole spacetime, irrespective of models. A time derivative form of the generalized second law is formulated and it is shown that the law might become invalid. The way to resolve this difficulty is also presented and discussed.